Proposition 2.2 (Theorem 1.2 in [1]}) 
Let \((M_{ext}, g)\)  be an exterior region of a complete AE Riemannian 3-manifold \((M,g)\)  with mass \(m(g)\) . Let \(u\)  be a harmonic function on \((M_{ext}, g)\)  asymptotic to one of the AE-coordinate functions of the associated end. Then
\(m(g) \ge \frac{1}{16\pi }\int _{{M_{ext}}} \left( \frac{|\nabla ^2 u|^2}{| \nabla u|} + R_g |\nabla u| \right) dV.\) 

